3D tamed Navier-Stokes equations driven by multiplicative L\'{e}vy noise: Existence, uniqueness and large deviations

TL;DR

This paper proves the existence, uniqueness, and large deviation principles for solutions to 3D tamed Navier-Stokes equations driven by multiplicative Lévy noise, advancing understanding of stochastic fluid dynamics under complex noise.

Contribution

It establishes the first rigorous results on existence, uniqueness, and large deviations for 3D tamed Navier-Stokes equations with multiplicative Lévy noise.

Findings

Existence and uniqueness of strong solutions are proven.

Large deviation principles are established for the solutions.

The weak convergence approach is employed for analysis.

Abstract

In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles of the strong solution on the state space $\mathcal{D}([0,T];\mathbb{H}^1)$, where the weak convergence approach plays a key role.